A non-commutative generalization of Lukasiewicz rings

作者：Kadji Albert; Lele Celestin; Nganou Jean B^*

来源：Journal of Applied Logic, 2016, 16: 1-13.

DOI：10.1016/j.jal.2016.04.001

• MV-algebra
• Lukasiewicz ring
• QF-ring
• Pseudo MV-algebra
• Semi-ring
• Special primary ring
• Dubrovin valuation ring
• Brown-McCoy radical
• Jacobson radical

The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Lukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.

• 出版日期2016-7